Of course in Italy they could use preexisting names. My question is aimed more at tre conquered provinces. Like for example in todays Western Germany a lot of names still show resemblance to the Roman names they were once given. Like Cologne or Mainz which where once named Colonia and Mogontiacum respectively. Both seem like decidetly latin names, so I assume that they didnt use the local names for those places. But if not then how did they name them? Did they just go wild like in the Settlers in the American west, where a settlement could be named after anything from the settlers last name to litteraly just the word Tombstone, or where there certain rules or practices that where followed?
There was no one way in which places were named as they got incorporated into the Roman orbit or sprang up over time. Sometimes they used functional descriptions, for example Chester in the U.K. gets its name from the Roman word Castrum - quite literally “fort” which is what it was. Other places used some form of their latinized name, possibly with a Roman addition, like Sarmizegetusa Regia in Dacia which carried a latinized form of its previous name plus “Regia” to denote its former status as the royal capital of pre-Roman Dacia. Others, like Antioch for example, kept their name since its earlier Greek spelling worked with Roman grammatical from and didn’t need to be latinized like others did.
Cologne was originally Oppidum Ubiorum - lit. Town of the Ubii, the local tribe - but when it was promoted to colonial status in the 1st century CE (a change affecting the rights of its inhabitants), its name was changed to Colonia Claudia Ara Agrippinensium (The Colony of Claudius and the Altar of the Agrippinians). This name change honored Agrippina the Yonger, wife of the Emperor Claudius, who had been born there. Over time, the only part of this that survived was Cologne, and this shortening is not uncommon.
For Mainz, Mogontiacum appears to have been a latinization if Mogons, the name of a local Celtic god. This name was also simplified over time.